The United boss expects versatile skipper Garner to move elsewhere in Vanarama National League North and defender Mills to potentially move up a division into a full-time environment.
Greene has also given goalkeeper Fabian Spiess an impending deadline to decide whether he wishes to remain with at the club.
The news comes off the back of midfielder Grant Roberts agreeing terms to remain with the Pilgrims.
Those already contracted for 2016-2017 include Joe Burgess, Callum Chippendale, Shane Clarke, Lewis Hilliard, Cameron Johnson, Jay Rollins and Courtney Wildin, with Kaine Felix agreeing to remain too.
Top goalscorer Dayle Southwell is expected to move on, albeit with the Pilgrims able to command a compensation fee for the 22-year-old.